# Size of variable arrays: sizeAlgebraic = 11 sizeStates = 6 sizeConstants = 15 from math import * from numpy import * def createLegends(): legend_states = [""] * sizeStates legend_rates = [""] * sizeStates legend_algebraic = [""] * sizeAlgebraic legend_voi = "" legend_constants = [""] * sizeConstants legend_voi = "time in component environment (second)" legend_states[0] = "q_Eb in component environment (fmol)" legend_states[1] = "q_NO in component environment (fmol)" legend_states[2] = "q_E6c in component environment (fmol)" legend_states[3] = "q_E5c in component environment (fmol)" legend_states[4] = "q_cGMP in component environment (fmol)" legend_states[5] = "q_NO_product in component environment (fmol)" legend_algebraic[6] = "v_R_1_sGC in component sGC (fmol_per_sec)" legend_algebraic[7] = "v_R_2_sGC in component sGC (fmol_per_sec)" legend_algebraic[8] = "v_R_3_sGC in component sGC (fmol_per_sec)" legend_algebraic[9] = "v_R_4_sGC in component sGC (fmol_per_sec)" legend_algebraic[10] = "v_R_DNO_sGC in component sGC (fmol_per_sec)" legend_constants[0] = "v_NO_generation in component environment (fmol_per_sec)" legend_constants[1] = "kappa_R_1_sGC in component sGC_parameters (fmol_per_sec)" legend_constants[2] = "kappa_R_2_sGC in component sGC_parameters (fmol_per_sec)" legend_constants[3] = "kappa_R_3_sGC in component sGC_parameters (fmol_per_sec)" legend_constants[4] = "kappa_R_4_sGC in component sGC_parameters (fmol_per_sec)" legend_constants[5] = "kappa_R_DNO_sGC in component sGC_parameters (fmol_per_sec)" legend_constants[6] = "K_Eb in component sGC_parameters (per_fmol)" legend_constants[7] = "K_NO in component sGC_parameters (per_fmol)" legend_constants[8] = "K_E6c in component sGC_parameters (per_fmol)" legend_constants[9] = "K_E5c in component sGC_parameters (per_fmol)" legend_constants[10] = "K_cGMP in component sGC_parameters (per_fmol)" legend_constants[11] = "K_NO_product in component sGC_parameters (per_fmol)" legend_constants[12] = "R in component constants (J_per_K_per_mol)" legend_constants[13] = "T in component constants (kelvin)" legend_algebraic[0] = "mu_Eb in component sGC (J_per_mol)" legend_algebraic[1] = "mu_NO in component sGC (J_per_mol)" legend_algebraic[2] = "mu_E6c in component sGC (J_per_mol)" legend_algebraic[3] = "mu_E5c in component sGC (J_per_mol)" legend_algebraic[4] = "mu_cGMP in component sGC (J_per_mol)" legend_algebraic[5] = "mu_NO_product in component sGC (J_per_mol)" legend_constants[14] = "F in component constants (C_per_mol)" legend_rates[0] = "d/dt q_Eb in component environment (fmol)" legend_rates[1] = "d/dt q_NO in component environment (fmol)" legend_rates[2] = "d/dt q_E6c in component environment (fmol)" legend_rates[3] = "d/dt q_E5c in component environment (fmol)" legend_rates[4] = "d/dt q_cGMP in component environment (fmol)" legend_rates[5] = "d/dt q_NO_product in component environment (fmol)" return (legend_states, legend_algebraic, legend_voi, legend_constants) def initConsts(): constants = [0.0] * sizeConstants; states = [0.0] * sizeStates; states[0] = 1e-18 states[1] = 0.00836 states[2] = 1e-18 states[3] = 1e-18 states[4] = 1e-18 states[5] = 1e-18 constants[0] = 0.000114 constants[1] = 996545 constants[2] = 0.00090595 constants[3] = 3.20816 constants[4] = 0.00996545 constants[5] = 0.0236081 constants[6] = 0.0638542 constants[7] = 0.114174 constants[8] = 29.7524 constants[9] = 0.297524 constants[10] = 0.269542 constants[11] = 0.0114174 constants[12] = 8.31 constants[13] = 310 constants[14] = 96485 return (states, constants) def computeRates(voi, states, constants): rates = [0.0] * sizeStates; algebraic = [0.0] * sizeAlgebraic algebraic[0] = constants[12]*constants[13]*log(constants[6]*states[0]) algebraic[1] = constants[12]*constants[13]*log(constants[7]*states[1]) algebraic[2] = constants[12]*constants[13]*log(constants[8]*states[2]) algebraic[6] = constants[1]*(exp((algebraic[0]+algebraic[1])/(constants[12]*constants[13]))-exp(algebraic[2]/(constants[12]*constants[13]))) algebraic[3] = constants[12]*constants[13]*log(constants[9]*states[3]) algebraic[7] = constants[2]*(exp(algebraic[2]/(constants[12]*constants[13]))-exp(algebraic[3]/(constants[12]*constants[13]))) algebraic[8] = constants[3]*(exp((algebraic[2]+algebraic[1])/(constants[12]*constants[13]))-exp((algebraic[3]+algebraic[1])/(constants[12]*constants[13]))) rates[2] = (algebraic[6]-algebraic[7])-algebraic[8] algebraic[4] = constants[12]*constants[13]*log(constants[10]*states[4]) algebraic[9] = constants[4]*(exp((algebraic[3]+algebraic[4]*2.00000)/(constants[12]*constants[13]))-exp((algebraic[0]+algebraic[1])/(constants[12]*constants[13]))) rates[0] = -algebraic[6]+algebraic[9] rates[3] = (algebraic[7]+algebraic[8])-algebraic[9] rates[4] = -2.00000*algebraic[9] algebraic[5] = constants[12]*constants[13]*log(constants[11]*states[5]) algebraic[10] = constants[5]*(exp(algebraic[1]/(constants[12]*constants[13]))-exp(algebraic[5]/(constants[12]*constants[13]))) rates[1] = ((-algebraic[6]+algebraic[9])-algebraic[10])+constants[0] rates[5] = algebraic[10] return(rates) def computeAlgebraic(constants, states, voi): algebraic = array([[0.0] * len(voi)] * sizeAlgebraic) states = array(states) voi = array(voi) algebraic[0] = constants[12]*constants[13]*log(constants[6]*states[0]) algebraic[1] = constants[12]*constants[13]*log(constants[7]*states[1]) algebraic[2] = constants[12]*constants[13]*log(constants[8]*states[2]) algebraic[6] = constants[1]*(exp((algebraic[0]+algebraic[1])/(constants[12]*constants[13]))-exp(algebraic[2]/(constants[12]*constants[13]))) algebraic[3] = constants[12]*constants[13]*log(constants[9]*states[3]) algebraic[7] = constants[2]*(exp(algebraic[2]/(constants[12]*constants[13]))-exp(algebraic[3]/(constants[12]*constants[13]))) algebraic[8] = constants[3]*(exp((algebraic[2]+algebraic[1])/(constants[12]*constants[13]))-exp((algebraic[3]+algebraic[1])/(constants[12]*constants[13]))) algebraic[4] = constants[12]*constants[13]*log(constants[10]*states[4]) algebraic[9] = constants[4]*(exp((algebraic[3]+algebraic[4]*2.00000)/(constants[12]*constants[13]))-exp((algebraic[0]+algebraic[1])/(constants[12]*constants[13]))) algebraic[5] = constants[12]*constants[13]*log(constants[11]*states[5]) algebraic[10] = constants[5]*(exp(algebraic[1]/(constants[12]*constants[13]))-exp(algebraic[5]/(constants[12]*constants[13]))) return algebraic def solve_model(): """Solve model with ODE solver""" from scipy.integrate import ode # Initialise constants and state variables (init_states, constants) = initConsts() # Set timespan to solve over voi = linspace(0, 10, 500) # Construct ODE object to solve r = ode(computeRates) r.set_integrator('vode', method='bdf', atol=1e-06, rtol=1e-06, max_step=1) r.set_initial_value(init_states, voi[0]) r.set_f_params(constants) # Solve model states = array([[0.0] * len(voi)] * sizeStates) states[:,0] = init_states for (i,t) in enumerate(voi[1:]): if r.successful(): r.integrate(t) states[:,i+1] = r.y else: break # Compute algebraic variables algebraic = computeAlgebraic(constants, states, voi) return (voi, states, algebraic) def plot_model(voi, states, algebraic): """Plot variables against variable of integration""" import pylab (legend_states, legend_algebraic, legend_voi, legend_constants) = createLegends() pylab.figure(1) pylab.plot(voi,vstack((states,algebraic)).T) pylab.xlabel(legend_voi) pylab.legend(legend_states + legend_algebraic, loc='best') pylab.show() if __name__ == "__main__": (voi, states, algebraic) = solve_model() plot_model(voi, states, algebraic)